document.write( "Question 147135: Find the verex and intercepts. Sketch the graph
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Algebra.Com's Answer #107556 by Edwin McCravy(20077)\"\" \"About 
You can put this solution on YOUR website!
Edwin's solution:\r
\n" ); document.write( "\n" ); document.write( "Find the verex and intercepts. Sketch the graph
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document.write( "The vertex formula:\r\n" );
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document.write( "The graph of \r\n" );
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document.write( "\"f%28x%29+=+ax%5E2%2Bbx%2Bc\"\r\n" );
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document.write( "has the vertex (\"-b%2F%282a%29\", \"-d%2F%284a%29\"), where \"d+=+discriminant+=+b%5E2-4ac\"\r\n" );
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document.write( "Therefore\r\n" );
document.write( "\"g%28x%29+=+x%5E2+-6\"\r\n" );
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document.write( "can be written as\r\n" );
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document.write( "\"g%28x%29+=+x%5E2%2B0x-6\"\r\n" );
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document.write( "So we apply the vertex formula:\r\n" );
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document.write( "\"a=1\", \"b=0\", \"c=-6\", \"d=discriminant=b%5E2-4ac=0%5E2-4%281%29%28-6%29=24\"\r\n" );
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document.write( "so the vertex is\r\n" );
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document.write( "(\"-b%2F%282a%29\", \"-d%2F%284a%29\") =\r\n" );
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document.write( "(\"-0%2F%282%281%29%29\", \"-24%2F%284%281%29%29\") = (\"0%29\", \"-6\")\r\n" );
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document.write( "To find the y-intercept, we substitute \"x=0\"\r\n" );
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document.write( "\"g%28x%29=+x%5E2+-6\"\r\n" );
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document.write( "\"g%280%29+=+0%5E2+-6\"\r\n" );
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document.write( "So the y-intecept is (\"0\", \"-6\"), which just happens\r\n" );
document.write( "to, in this case, be the same point as the vertex.\r\n" );
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document.write( "To find the x-intercepts, we we substitute \"g%28x%29=0\"\r\n" );
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document.write( "\"g%28x%29=+x%5E2+-6\"\r\n" );
document.write( "\"0=+x%5E2+-6\"\r\n" );
document.write( "\"-x%5E2=-6\"\r\n" );
document.write( "\"x%5E2=6\"\r\n" );
document.write( "\"x\" = ±\"sqrt%286%29\"\r\n" );
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document.write( "Since the square root of 6 is about \"2.45\",\r\n" );
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document.write( "the two x intercepts are about (\"-2.45\", \"0\") and (\"2.45\", \"0\")\r\n" );
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document.write( "So we plot those two points, as well as:\r\n" );
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document.write( "vertex: (\"0%29\", \"-6\")\r\n" );
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document.write( "and\r\n" );
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document.write( "y-intercept: (\"0%29\", \"-6\") [Which in this case just \r\n" );
document.write( "happens to be the same point as the vertex.]\r\n" );
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document.write( "Edwin
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